Math Properties

1. Math Properties A property is something that is true for all situations.

2. Six Properties • Distributive • Commutative • Associative • Identity properties of one and zero • Inverse Property • Zero Property

3. Distributive Property To multiply a sum or difference. Multiply each number within the parentheses by the number outside the parentheses. 4(3 + 5) = 4x3 + 4x5 A(B + C) = AB + AC

4. Commutative Propertyof addition and multiplication Order doesn’t matter A x B = B x A 5 x 2 = 2 x 5 A + B = B + A 8 + 3 = 3 + 8

5. Associative Property of multiplication and Addition Grouping doesn’t change the answer Associative Property  (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) Associative Property  (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3)

6. Identity Properties If you add 0 to any number, the number stays the same. A + 0 = A or 5 + 0 = 5 If you multiply any number times 1, the number stays the same. A x 1 = A or 5 x 1 = 5

7. Inverse Property Addition: two numbers whose sum is zero Example: 6 + -6 = 0 h + -h = 0 Multiplication: two numbers whose product is one Example: 3 x (1/3) = 1 j x (1/j) = 1

8. Zero Property When multiplying, any number times zero is zero example: 24 x 0 = 0 k x 0 = 0